Decimal places and significant figures
There are two common ways to round a number at GCSE:
- Decimal places (d.p.) — count digits after the decimal point
- Significant figures (s.f.) — count digits starting from the first non-zero digit, from the left, regardless of the decimal point's position
Both use the same rule: look at the digit after the one you're rounding to. If it's 5 or more, round up; if it's less than 5, round down (and every digit after the rounding point is removed).
Rounding to decimal places
Worked Example 1
Round 7.3846 to 2 decimal places.
1
Identify the 2nd decimal digit (the one you're rounding to): 7.3846
2
Look at the next digit (the 3rd decimal place): 4 — this is less than 5, so round down (keep the 8 as it is)
Answer7.38
Rounding to significant figures
Worked Example 2
Round 258 to 1 significant figure.
1
The first significant figure is the 2 (in the hundreds column)
2
Look at the next digit: 5 — this means round up, so 2 becomes 3
3
Replace all remaining digits with placeholder zeros to keep the correct size: 300
Answer300
Worked Example 3
Round 0.004567 to 2 significant figures.
1
Leading zeros don't count — the first significant figure is 4, the second is 5: 0.004567
2
Look at the next digit: 6 — round up, so 45 becomes 46
Answer0.0046
Leading zeros (0.00) are placeholders, not significant figures — counting starts at the first non-zero digit.
Estimating a calculation
To estimate the answer to a calculation, round every number to 1 significant figure first, then calculate with the simplified numbers. This gives a quick, approximate check of the correct order of magnitude.
Worked Example 4
Estimate the value of 396 × 0.52, by rounding each number to 1 significant figure.
1
Round 396 to 1 significant figure: 400
2
Round 0.52 to 1 significant figure: 0.5
3
Multiply the rounded values: 400 × 0.5 = 200
Answer≈ 200 (the exact value is 205.92)
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1Round 5.638 to 1 decimal place.Foundation
Q2Round 12.95 to 1 decimal place.Foundation
Q3Round 4728 to 2 significant figures.Foundation
Q4Round 0.0362 to 1 significant figure.Foundation
Q5Estimate 58 × 21, by rounding each number to 1 significant figure.Foundation
Higher (Grade 5–7)
Q6Round 6.0489 to 3 decimal places.Higher
Q7Round 39,650 to 3 significant figures.Higher
Q8Round 0.019876 to 2 significant figures.Higher
Q9Estimate the value of (203 × 48) ÷ 9.8, by rounding each number to 1 significant figure.Higher
Q10Round 999.96 to 1 decimal place.Higher
Higher — Hard (Grade 8–9)
Q11Round 0.00099951 to 3 significant figures.Grade 8–9
Q12Estimate 4.87 × 10⁶ ÷ 2.3 × 10⁻², by rounding each number to 1 significant figure, giving your answer in standard form.Grade 8–9
Q13A room measures 4.6m by 3.2m. Estimate its area by rounding each measurement to 1 significant figure.Grade 8–9
Q14Round 149.5 to the nearest 10.Grade 8–9
Q15A student estimates 6.8 × 9.3 as 7 × 9 = 63. Calculate the exact value and comment on whether the estimate was a reasonable check.Grade 8–9
Answers
Foundation (Q1–Q5)
Q15.6
Q213.0(the second decimal, 5, rounds the 9 up, carrying to the units column)
Q34700
Q40.04
Q51200(60 × 20; exact value is 1218)
Higher (Q6–Q10)
Q66.049
Q739,700
Q80.020
Q91000(200 × 50 ÷ 10; exact value is approximately 994.3)
Q101000.0(the second decimal, 6, rounds 9 up, which carries all the way through: 999.96 → 1000.0)
Higher — Hard (Q11–Q15)
Q110.00100(the three nines round up to 1000, since the next digit is 5)
Q122.5 × 10⁸(5 × 10⁶ ÷ 2 × 10⁻² = 2.5 × 10⁸)
Q1315 m²(5m × 3m; exact value is approximately 14.72 m²)
Q14150
Q15Exact value: 63.24. The estimate of 63 is very close to the exact answer, so it's a reasonable check that the calculation is roughly correct.
Common mistakes
Common Mistake 1
Confusing decimal places with significant figures
0.0362 to 1 decimal place is 0.0, but to 1 significant figure it's 0.04 — these give completely different answers, so always check exactly which rounding method the question asks for.
Common Mistake 2
Counting leading zeros as significant figures
In 0.004567, the zeros before the 4 are not significant figures — they're placeholders. Significant figures always start counting from the first non-zero digit.
Common Mistake 3
Forgetting placeholder zeros after rounding
Rounding 258 to 1 significant figure gives 300, not 3 — the placeholder zeros are needed to keep the number the correct size.
Common Mistake 4
Rounding each part of a calculation separately, using different accuracies
For estimation, round every number in the calculation to 1 significant figure before calculating — mixing accuracies partway through gives an unreliable estimate.
Exam tips
💡 Exam Tip 1
Underline the digit you're rounding to
Physically underlining or circling the digit you're rounding to, then checking the digit immediately after it, removes almost all careless rounding errors.
💡 Exam Tip 2
Watch for rounding that carries through several digits
Numbers like 999.96 or 19.98 can carry all the way through several digits when rounded — don't assume only the digit you're rounding will change.
💡 Exam Tip 3
Use estimation to sense-check your working
Before submitting a calculator answer, do a quick 1-significant-figure estimate. If your calculator answer is wildly different from the estimate, you've likely mistyped something.
💡 Exam Tip 4
State the accuracy in your final answer
If a question specifies "to 2 decimal places" or "to 3 significant figures", make sure your final written answer actually matches that accuracy — don't leave extra or missing digits.
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